Mixed-integer nonlinear optimal control

Although, as explained in Chapter 9, many optimization problems can be naturally formulated as mixed-integer programming problems, in this chapter we will consider only steady-state nonlinear programming problems in which the variables are continuous. In some cases it may be feasible to use binary variables (on-off) to include or exclude specific stream flows, alternative flowsheet topography, or different parameters. In the economic evaluation of processes, in design, or in control, usually only a few (5-50) variables are decision, or independent, variables amid a multitude of dependent variables (hundreds or thousands). The number of dependent variables in principle (but not necessarily in practice) is equivalent to the number of independent equality constraints plus the active inequality constraints in a process. The number of independent (decision) variables comprises the remaining set of variables whose values are unknown. Introduction into the model of a specification of the value of a variable, such as T = 400°C, is equivalent to the solution of an independent equation and reduces the total number of variables whose values are unknown by one. 

H. H. Hoang. Topological optimization of networks A nonlinear mixed integer model employing generalized Benders decomposition. IEEE Trans. Automatic Control, AC-27 164, 1982. 

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